ORLANDO, Fla. — Perhaps one reason Carmelo Anthony was so moved by new coach Jeff Hornacek watching his recent workouts is the new Knicks coach traveled into Manhattan to do so.

Hornacek watched a couple of Anthony’s sessions at Anthony’s own gym, Terminal 23, in midtown — not at the club’s Tarrytown facility. They talked afterward — with Hornacek already offering him tips. Anthony said at Monday’s U.S. Olympic Team press conference he genuinely was appreciative of Hornacek’s gesture.

“I watched his workout and put my two cents in there,” Hornacek said. “I talked to him about what went on in the last couple of years, what he sees for this coming year, what he’d like to see. Watching tape, I said there were couple of things I can help him. I try to talk to all the players. Get a sense of what worked well, what didn’t and try to blend something.”

Hornacek mentioned last week before the draft he has noticed Anthony wasn’t always out on the fast break — a team emphasis this season. He has shared this with Anthony.

“His shooting is fine, it’s more positioning on the court,” Hornacek said. “I told him we’re going to try to push the ball more, so you’re going to have to get the ball up the court quicker. There were situations, if you were a little bit quicker down the court, the shot would’ve ended up coming to you. A little thing to think about over the summer.”

And a big moment in Anthony’s eyes.

Point guard Tony Wroten, waived last week by the Knicks, was claimed this week by Memphis, but a source said he won’t play in the summer league as he had planned.

Wroten reportedly was waived not just because of his major knee problems but because of a disciplinary issue. The Post reported last month Wroten has two ACL surgeries in his past — not just one. A source told The Post Wroten had disciplinary issues with the Sixers, who waived him last December. Greg Lawrence, Wroten’s agent, did not return phone calls.